Respuesta :
Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.
How to calculate the standard deviation of a data set?
Step 1: Find the mean
Step 2: Find each score’s deviation from the mean
Step 3: Square each deviation from the mean
Step 4: Find the sum of squares
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}[/tex]
The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.
Step 1: Find the mean
The mean of the given data set can be written as,
[tex]Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857[/tex]
Step 2: Find each score’s deviation from the mean
1 - 3.857 = -2.857
4 - 3.857 = 0.143
2 - 3.857= -1.857
2 - 3.857= -1.857
8 - 3.857 = 4.143
7 - 3.857 = 3.143
3 - 3.857 = -0.857
Step 3: Square each deviation from the mean
-2.857² = 8.162
0.143² = 0.02
-1.857² = 3.447
-1.857² = 3.447
4.143² = 17.165
3.143² = 9.877
-0.857²= 0.735
Step 4: Find the sum of squares
8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857
Step 5: Apply the formula
[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474[/tex]
Hence, the standard deviation of the data set is 2.474.
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